Structural shape determination under uncertain loading conditions

Abstract

A method for the dertermination of the shape of structures is formulated in the case when the directions, positions or magnitudes of loads vary with a known probability law. By extending the criterion of the inverse-variational-problem that was proposed in the case of determinate loading conditions, the shape of a body, for which the expected value of the potential energy becomes stationary among all shapes with the same volume, is determined. For the optimization problem, displacements are assumed to be expressed as random variables. Then, a factorization of the variable loads into several fundamental loads is proposed in order to reduce the computational effort. Structures with considerably improved performance can be easily obtained, for the uncertain loading, by the present method.